Question

a ski slope has an angle of elevation of 23°.
a which ratio would you use to determine the height of the ski slope? explain your choice.

Explanation:

We are working with a right triangle where we know the angle of elevation ($23^\circ$), the adjacent side to this angle (3076 ft, the horizontal length), and $x$ is the opposite side (the height of the slope). The tangent function relates the opposite and adjacent sides of a right triangle for a given angle, so we use $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$.

Answer:

We use the tangent ratio. For the given $23^\circ$ angle, the height $x$ is the opposite side, and 3076 ft is the adjacent side to the angle. The tangent of an angle in a right triangle is defined as the ratio of the length of the opposite side to the length of the adjacent side, so $\tan(23^\circ) = \frac{x}{3076}$ is the correct ratio to solve for the height.